一个四元组合问题的研究  

Study On a Four-place Combination

作　　者：陈伟侯[1] 张录达[1] 朱正元[2] 

机构地区：[1]中国农业大学理学院,北京100094 [2]中央民族大学数学与计算机科学学院,北京100081

出　　处：《中央民族大学学报（自然科学版）》2005年第3期220-223,共4页Journal of Minzu University of China(Natural Sciences Edition)

摘　　要：从1到13这13个正整数中任意取四个(可以重复),构成一个四元组合.对每一个四元组合,任意选用+,-,×,÷及表示二元运算顺序的括号可以构成大量的算式.本文给出了:A.枚举全体四元组合的算法;B.枚举某个四元组合全体算式的算法.用这两个算法对二十四点游戏的基本特征进行了研究,并用列表法给出共有1820个自变量值的功效函数.这个功效函数为进一步研究二十四点游戏建立了基础.The four numbers, selected arbitrarily from the integer number 1 to 13, construct a four-place combination, and the numbers can be reused. The four numbers can be constituted to an algebraic expression by choosing arbitrarily the sign ＂ ＋ ＂, ＂ - ＂, ＂ x ＂, ＂ ÷ ＂, and the bracket ＂（ ）＂ In the article, two enumeration algorithms, constructing a four-place combination and getting all the algebraic expressions for a four-place combination, are introduced. Also, the element features of the ‘24 points game＇ are studied with two algorithms. A utility function with 1820 independent variable value is listed in a table. The utility function would contribute to further research of the ‘24 points game＇ .

关 键 词：二十四点游戏 四元组合 枚举算法 功效函数 

分 类 号：O157[理学—数学]